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AURORKA [14]
3 years ago
13

Solve (x + 4)2 – 3(x + 4) – 3 = 0 using substitution.

Mathematics
2 answers:
BaLLatris [955]3 years ago
7 0

I would say that the answer is B

Alenkasestr [34]3 years ago
5 0

Answer:

Option B is correct.

u= x+4

Step-by-step explanation:

Solve the equation:

(x+4)^2-3(x+4)-3 = 0

Using substitution:

Let u = x+4

then;

u^2-3u-3=0         ....[1]

For a quadratic equation ax^2+bx+c = 0 ....[2], then the solution is given by:

x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}

On comparing equation [1] and [2] we have;

a = 1 , b = -3 and c = -3

then;

u= \frac{-(-3) \pm \sqrt{(-3)^2-4(1)(-3)}}{2(1)}

⇒u= \frac{3 \pm \sqrt{9+12}}{2}

⇒u= \frac{3 \pm \sqrt{21}}{2}

Substitute u = x+4

then;

⇒x+4= \frac{3 \pm \sqrt{21}}{2}

Subtract 4 from both sides we have;

x= \frac{3 \pm \sqrt{21}}{2} - 4= \frac{3 \pm \sqrt{21}-8}{2}

⇒x= \frac{3 + \sqrt{21}-8}{2}= \frac{-5 + \sqrt{21}}{2}

and

x= \frac{3 - \sqrt{21}-8}{2}

⇒x= \frac{-5 - \sqrt{21}}{2}

Therefore, the solution for the given equation are,

x= \frac{-5 - \sqrt{21}}{2} , \frac{-5 + \sqrt{21}}{2}

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=================================================

Work Shown:

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